Does your character have any immunity or defense against being empathically read? Nope, go nuts.
Is there any particular pain and/or memory you would like Cole to pick up on first or focus on? Her grief/survivor's guilt about those of her company lost at the Conclave, and similar feelings about having been present for that last night in Haven.
Is there anything else that can be found in their app or wiki pages that should remain off-limits? Not really, no. Anything in her app or navigation page is fair game.